A consistent consequence of AD

Bull, E. L.; Kleinberg, E. M.

doi:10.1090/S0002-9947-1979-0517692-2

A consistent consequence of AD
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by E. L. Bull and E. M. Kleinberg PDF

Trans. Amer. Math. Soc. 247 (1979), 211-226 Request permission

Abstract:

We are concerned with the existence of a normal measure concentrating on the $\omega$-closed unbounded sets. We strengthen the known result that the axiom of choice implies no such measure exists. It is shown that the existence of these measures is consistent (relative to a large cardinal). In particular, ${\aleph _2}$ may admit exactly two normal measures: one which contains the $\omega$-closed unbounded sets and the other, the ${\aleph _1}$-closed unbounded sets. This property of ${\aleph _2}$ is a well-known consequence of AD.

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